BAGHDAD, Iraq (CNN) -- The top U.S. commander in Iraq, Gen. David Petraeus, said Iran continues to support Iraqi insurgents and Syria is allowing foreign fighters passage into Iraq.

Gen. David Petraeus speaks to CNN's Kyra Phillips on Wednesday in Baghdad, Iraq.

"We are concerned very much about the lethal accelerants, as they are called, that do come from Iran," he said. "And we appropriately raise that to those who have a broader perspective, then, who have a regional and then a global look.

"And the same way that we do about what comes through Syria."

The general's comments about Iran come just a day after Sen. John McCain, R-Arizona, the presumptive Republican presidential nominee, said there are continued fears that Iran may be training Iraqi extremists in Iran and sending them back to Iraq.

McCain expressed concern about a large cache of explosives found in Iraq and hinted that they may have been sent from Iran.

In January, Petraeus said attacks against U.S. troops in Iraq with bombs believed linked to Iran -- known as explosively formed penetrators (EFPs) -- had risen sharply after several months of decline. But that came after several months of decline in Iranian involvement.

The Bush administration and the military have long maintained that Iranian agents, particularly the Quds Force of Iran's Islamic Revolutionary Guard Corps, have been arming and training Iraqi insurgents.

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Iranian President Mahmoud Ahmadinejad visited Iraq earlier this month and pledged to help Iraq with energy supplies, while denouncing U.S. statements about Iranian involvement with Iraqi insurgents.

"We do not care about their statements and remarks because they make statements based on erroneous information. We cannot count on what they say," Ahmadinejad said.

Differences with the Bush administration over Iran were reported to be behind the resignation of Petraeus' boss, Adm. William Fallon, earlier this month, but Petraeus on Wednesday said he and Fallon have been seeing eye-to-eye on Iraq in recent months.

Petraeus is scheduled to appear before Congress in April to testify about the progress of the war, which began five years ago Wednesday.

He said most of the additional U.S. troops Bush ordered into Iraq last year will be coming home by late summer, but future withdrawals will depend on whether improvements in security in and around Baghdad continue to hold.

"We're keenly aware of the strain that this has put on the force, the sacrifices of the families back home; on our troops," he said. "And we want to continue, obviously, to draw down our forces in the months after that, but we do want to do it in a way that, again, does not place in jeopardy all that we've fought so hard for, particularly over the course of this past year."

Shiite PM visits Sunni area of Baghdad

In Baghdad on Wednesday, Iraq's Shiite Prime Minister Nuri al-Maliki visited a Sunni stronghold in the northern part of the city as part of a push toward national reconciliation.

The visit to Adhamiya, al-Maliki's first since becoming Iraq's prime minister in 2006, is to commemorate the birth anniversary of the Prophet Mohammed, which falls on Thursday.

Adhamiya is a center for Sunni Arabs who were loyal to executed Iraqi dictator Saddam Hussein, and is a former stronghold for al Qaeda in Iraq insurgents.

The neighborhood is now controlled by local Awakening Councils, which are Sunni groups who have turned against al Qaeda in Iraq.

While the Muslim prophet's birthday falls on Thursday, most Iraqis celebrate the anniversary on Wednesday night.

Al-Maliki's government has been hamstrung from achieving political progress on key issues -- including the distribution of oil wealth -- because of ethnic tensions among Iraqis, particularly between Shiite and Sunni Muslims.

Shiite-Sunni tensions ignited into widespread violence after the February 2006 bombing of the Golden Mosque, a famous Shiite mosque in Samarra.

Deadly incident

Also Wednesday, a U.S. soldier died after a vehicle rollover in Diyala province, the military said.

Diyala stretches north and east of Baghdad and has been a major front in the war during the escalation of U.S. troops who have been taking on insurgents near the capital.

The death brings the total number of U.S. casualties in the war to 3,992.E-mail to a friend